It's become fashionable in certain circles to have a go at HS2, the proposed high-speed rail line linking London, Birmingham, Sheffield, Leeds and Manchester.

The former Labour business secretary Lord Mandelson is the latest to join a motley coalition of self-interested nimbys and metropolitan snobs who don't seem to like the idea of the barbarian north having access to the capital in less time than it takes to play a professional football match.

Speaking on Wednesday, Mandelson said High Speed 2 was an "expensive mistake" and that the economic case for pressing ahead was "neither quantified nor proven". He also suggested the policy had been "politically driven" by the last Labour government to "paint an upbeat view of the future" following the financial crash in 2008.

And yet HS2 is exactly the kind of major infrastructure project that is needed to kickstart our moribund economy, with projections that 100,000 jobs – many in highly skilled engineering and design roles – will be created. Therefore the process of actually building the line is a significant result in itself.

Once completed, 18 trains an hour, each taking up to 1,100 passengers, will run from northern cities to London and vice versa, taking nearly 10 million car journeys off the road. This won't "damage" the north of England's economy as Mandelson believes, it will rejuvenate it.

But the real reason HS2 is so badly needed is that passenger numbers have doubled in the past two decades, leaving existing infrastructure badly overstretched. A new line will free up space for more local passenger and freight services. Without HS2, these services risk being squeezed out as intercity services take priority. So people travelling between our great cities are set to benefit from HS2, but so, too, will people using local rail services.

HS2 Limited, the company managing the construction of the line, reckons it will improve connectivity between eight of our ten biggest cities, generating an economic return of £2 for every £1 invested in the project. The tens of thousands of new jobs that will be created will be spread along the route and British industry will gain valuable expertise in high-speed rail, a growing international market.

Yet opponents still question the economic case. John Tomaney from University College London suggests that London, rather than the north, will benefit most by making it easier to suck-in talent and investment to the capital from farther afield. But there is absolutely no reason why this should be the case; quite the reverse.

Britain is the most needlessly centralised country in the developed world, with an overheating and increasingly inefficient London becoming a stifling and extremely expensive place to do business. HS2 will give investors the proximity they crave without the ludicrous costs of locating within the M25.

Of course HS2 will also slash journey times between London and Birmingham, Manchester, Sheffield and Leeds and other cities as far north as Edinburgh and Glasgow. This has been dismissed by some opponents, including the prime minister's father-in-law, Lord Astor, as a frippery. "Have they not heard of Skype and the internet?" he helpfully suggested as an alternative to actual travel.

What we do know with certainty is that following HS2's construction towns such as Crewe become London commuter suburbs overnight, with journey times to the capital cut to just 58 minutes.

It opens up the prospect of an end to the brain drain that traditionally sees talented people from the north – from across all walks of life – face the dilemma of relocating to the south-east to follow work opportunities, or stay in the north and have a better quality of life. HS2 means having the best of both worlds: a London-based career with a northern home life.

So despite its detractors' claims, HS2 will open up new possibilities for people and businesses at either end of the line and do more to eradicate the North-South divide than any other measure in the last 50 years.

Of course, as the minister who landed us with the £900 million Millennium Dome, Peter Mandelson knows a thing or two about "expensive mistakes", but when it comes to high speed rail, its time the Prince of Darkness and his friends saw the light.